Anytime people get mad at the metrologist for being wrong, I remind them that they're LITERALLY PREDICTING THE FUTURE.

As someone trained in statistics, I will say you have nailed this. The only 'poll' that has any hope of being accurate is counting the votes the day after. Even if we had good models for the complex intricacies of human behavior with respect to voting (I will correct that we do have good models of human behavior, Game Theory and Network Theory have gone a long way towards providing workable models for things) there is no way to guarantee clean input data. Garbage in, conservatives out. Pollster bias, population bias, selection bias, social pressures causing disingenuous responses. You can't get away from any of it. Phone polling requires that people answer and actually participate, which eliminates swaths of personality types which skews your data. In-person polls have to be conducted in person, so the location choice skews the types of people who are likely to be present at the time you are polling. Even focus groups are inherently flawed as a polling methodology, but they are as close to clean as one can get. You still only obtain the opinions of people who have the time during the day to go somewhere for hours. So it is predominantly young college students between classes, stay-at-home parents while the kids are in school, people who are unemployed, or retirees looking for something to do. If it is not one of those, it is likely someone who is doing the focus groups to make ends meet and the repeated use of the same people for different polls often leads to other forms of data contamination.

Bottom line, don't trust polls. If you aren't doing them, likely the demographics that you represent are not doing them either.

Another issue that affects how accurately weather models are seen is a difference in what they output and what is reported. The output of the models is a series of 2D maps of various variables and how they change over time and space. The models will predict that conditions will form for cloud formation and will lead to precipitation at a certain point. They are pretty good at predicting that part. Where it starts to get less accurate is determining where those things will happen and when with specificity. They'll be pretty sure that there will be rain from this particular system, but it might move north of city x, go right over it, or go south of it.

So that 40% chance of rain is actually "99% chance it rains, but 39.5% chance it rains here and 59.5% chance it doesn't rain here but somewhere else nearby instead".

My appreciation for what they do increased after I started using windy.com, which gives the map of predictions over time instead of "here's what will happen in this city".

Oh and weather patterns can be smaller than cities, too. That 40% chance of rain could even mean "40% of the city will be rained on". On cloudy days, you can often look around and see rain in the distance in various directions around you, sometimes it passes over you sometimes it doesn't.